Link travel times in congested urban road networks are highly stochastic. Many empirical studies have found that travellers on such networks prefer to choose reliable shortest paths (RSP) for their travel so that they can arrive at destinations with a higher on-time arrival probability. Therefore, it is necessary to investigate the problems of finding these RSP in realistic road networks with travel time uncertainties. It is acknowledged that the RSP problems are significant; nonetheless few effective and efficient methods have been recorded in the literature. This is mainly due to the non-additive objective function of the RSP problems. Classical shortest path algorithms, built on the additive property, cannot be used to solve the RSP problems. In view of the above, the research presented in this thesis reveals model and solution algorithm for solving such RSP problems together with illustrations of their applicability in various transportation fields. This thesis contributes to the literature of RSP problems in several aspects. Firstly, a multi-criteria shortest path-finding model is proposed to tackle the non-additive difficulty involved in RSP problems. Several dominance conditions of the RSP problems are established to enable the use of generalized dynamic programming approaches for solving the RSP problems. In the proposed RSP model, the travel time spatial correlations among k-neighboring links are considered. This limited travel time spatial dependence can be interpreted as Tobler's First Law of Geography that "all things are related, but nearby things are more related than distant things". An efficient multi-criteria A* algorithm is proposed to determine the RSP without the requirement of generating all non-dominated paths in the entire network. A case study using traffic data from a real-world advanced traveller information system (ATIS) is provided to validate the proposed solution algorithm.The proposed RSP model and solution algorithm are extended to incorporate travel time temporal correlations in those stochastic time-dependent (STD) networks where link travel time distributions vary by time intervals throughout the day. In the STD networks, travellers' experienced link travel time variation depends on the time instance vehicles entering the link; and the link travel time distribution is typically assumed to be fixed when these vehicles travelling on that link. This assumption, however, may violate the first in first out (FIFO) property, since traffic conditions cannot be updated when vehicles travelling on the link. To address this non-FIFO problem, a stochastic travel speed model (S-TSM) that can update travellers' experienced travel speeds during different time intervals on the link is proposed in this research. The proposed S-TSM can ensure the FIFO property of link travel times, so that the efficient multi-criteria A* algorithm can be adopted to solve the RSP problems in STD networks. Based on the proposed multi-criteria A* algorithm, a real-world ATIS-based routing system is developed to aid road users of Hong Kong making route choice decisions in road networks with travel time spatiotemporal correlations. Secondly, the proposed RSP model is incorporated in reliability-based user equilibrium (RUE) problems for traffic assignment. In this research, an effective reliable shortest path algorithm is developed to determine RSP for all user classes in one search process so as to avoid the repeated path searching for each user class. The proposed reliable shortest path algorithm is then, further incorporated into a path-based RUE assignment algorithm using a column generation method. The proposed RUE assignment algorithm does not require path enumeration and can achieve highly accurate RUE results within reasonable computational time. A numerical example demonstrates that the proposed RUE assignment algorithm is capable for solving relevant problems in road networks with demand and / or supply uncertainties. Thirdly, the proposed RSP and RUE algorithms are applied to identify critical links in large-scale road networks. The traditional method, to identify critical links, is to use a full scan approach to assess all possible link closure scenarios by means of traffic assignment methods. This full scan approach is not viable for identifying critical links in large-scale road networks, because of the large number of link closure scenarios and computational intensity of traffic assignment methods in these large-scale networks. An impact area vulnerability analysis approach is proposed in this research to evaluate the consequences of a link failure within a local impact area, rather than the entire network. Such vulnerability analysis approach reduces the problem size of the critical link identification so as to reduce the computational burden involved. Case studies on large-scale real-world networks are presented to illustrate the proposed impact area vulnerability approach and investigate the effects of stochastic demand and heterogeneous travellers' risk-taking behaviour.

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